10^3x = 55^1
3x = 55
x = 18.333 ---> I attempted to correct this and came up with x = log(10)55/3. I still resulted with x = 18.333 and I don't understand why this was still marked wrong.

Thanks in advance.

Is this 10^(3x) = 55 or 10^(3) * x = 55? The notation you used was a bit unclear. But I'm going to assume you mean 10^(3x) = 55.

From this, you CANNOT say that 3x = 55. You can't set the exponent of the left hand side equal to the base of the right hand side (doing so is invalid and makes no sense). However, we can solve for x by taking the log of both sides: